Logistic Regression and Residual Analysis

Lecture 05

Dr. Colin Rundel

Last time

Last time

aids
# A tibble: 13 × 2
    year cases
   <int> <int>
 1  1981    12
 2  1982    14
 3  1983    33
 4  1984    50
 5  1985    67
 6  1986    74
 7  1987   123
 8  1988   141
 9  1989   165
10  1990   204
11  1991   253
12  1992   246
13  1993   240

Model Fit

g = glm(cases~year, data=aids, family=poisson)
g_pred = broom::augment(
  g, type.predict = "response", 
  newdata = tibble(year=seq(1981,1993,by=0.1))
)
g

Call:  glm(formula = cases ~ year, family = poisson, data = aids)

Coefficients:
(Intercept)         year  
  -397.0594       0.2021  

Degrees of Freedom: 12 Total (i.e. Null);  11 Residual
Null Deviance:      872.2 
Residual Deviance: 80.69    AIC: 166.4

Bayesian Poisson Regression Model

( g_bayes = brms::brm(
    cases~year, data=aids, family=poisson,
    refresh=0, backend = "cmdstanr"
) )
 Family: poisson 
  Links: mu = log 
Formula: cases ~ year 
   Data: aids (Number of observations: 13) 
  Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
         total post-warmup draws = 4000

Population-Level Effects: 
          Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept  -396.97     15.07  -427.48  -368.01 1.00     1638     1965
year          0.20      0.01     0.19     0.22 1.00     1639     2007

Draws were sampled using sample(hmc). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).

Model fit

Model performance - rmse, crps

predicted_draws_fix(g_bayes, newdata = aids) |>
  group_by(.chain, .row) |>
  summarize(
    rmse = yardstick::rmse_vec(cases, .prediction),
    crps = dukestm::calc_crps(.prediction, cases)
  ) |>
  group_by(.chain) |>
  summarize(
    rmse = mean(rmse),
    crps = mean(crps)
  )
# A tibble: 4 × 3
  .chain  rmse  crps
   <int> <dbl> <dbl>
1      1  26.2  17.6
2      2  26.2  17.5
3      3  26.3  17.7
4      4  26.3  17.6

Model performance - emp coverage

predicted_draws_fix(g_bayes, newdata = aids) |>
  group_by(.row, cases) |>
  ggdist::mean_hdi(
    .prediction, .width = c(0.5,0.9,0.95)
  ) |>
  mutate(contains = cases >= .lower & cases <= .upper) %>%
  group_by(.width) |>
  summarize(
    emp_cov = sum(contains)/n()
  )
# A tibble: 3 × 2
  .width emp_cov
   <dbl>   <dbl>
1   0.5    0.231
2   0.9    0.385
3   0.95   0.462

Updating the model

Quadratic fit

g2 = glm(cases~year+I(year^2), data=aids, family=poisson)

g2_pred = broom::augment(
  g2, type.predict = "response",
  newdata=tibble(year=seq(1981,1993,by=0.1))
) 

Quadratic fit - residuals

Bayesian quadratic fit

( g2_bayes = brms::brm(
  cases~year+I(year^2), data=aids, family=poisson,
  refresh=0, backend = "cmdstanr"
) )
 Family: poisson 
  Links: mu = log 
Formula: cases ~ year + I(year^2) 
   Data: aids (Number of observations: 13) 
  Draws: 1 chains, each with iter = 2000; warmup = 1000; thin = 1;
         total post-warmup draws = 1000

Population-Level Effects: 
          Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept   756.71     21.92   713.71   796.44 1.17        6       17
year         -0.96      0.02    -1.00    -0.92 1.22        4       21
IyearE2       0.00      0.00     0.00     0.00 1.19        5       14

Draws were sampled using sample(hmc). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).

Diagnostics

plot(g2_bayes)

PP Checks

brms::pp_check(g2_bayes, ndraws=100)

Bayesian quadratic fit (fixed)

( g2_bayes = brms::brm(
  cases~I(year-min(year))+I((year-min(year))^2), data=aids, family=poisson,
  refresh=0, backend = "cmdstanr"
) )
 Family: poisson 
  Links: mu = log 
Formula: cases ~ I(year - min(year)) + I((year - min(year))^2) 
   Data: aids (Number of observations: 13) 
  Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
         total post-warmup draws = 4000

Population-Level Effects: 
                Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept           2.43      0.14     2.14     2.71 1.00     1025     1238
IyearMminyear       0.52      0.04     0.44     0.59 1.00     1025     1389
IyearMminyearE2    -0.02      0.00    -0.03    -0.02 1.00     1066     1402

Draws were sampled using sample(hmc). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).

Diagnostics

plot(g2_bayes)

PP Checks

brms::pp_check(g2_bayes, ndraws=100)

Model fit - \(Y\) CI

aids_base +
  tidybayes::stat_lineribbon(
    data = g2_bayes_pred, aes(y=.prediction), alpha=0.25
  )

Residuals (pearson)

residual_draws_fix(g2_bayes, newdata = aids, type = "pearson") |> 
  ggplot(aes(y = .residual, x = year, color=as.factor(.chain), group=.chain)) +
    tidybayes::stat_pointinterval(alpha=0.2) +
    geom_hline(yintercept = 0, color='grey', linetype=2)

Model performance - rmse, crps

predicted_draws_fix(g2_bayes, newdata = aids) |>
  group_by(.chain, .row) |>
  summarize(
    rmse = yardstick::rmse_vec(cases, .prediction),
    crps = calc_crps(.prediction, cases)
  ) |>
  group_by(.chain) |>
  summarize(
    rmse = mean(rmse),
    crps = mean(crps)
  )
# A tibble: 4 × 3
  .chain  rmse  crps
   <int> <dbl> <dbl>
1      1  14.2  5.15
2      2  14.2  5.16
3      3  14.3  5.18
4      4  14.1  5.14

Model performance - emp coverage

predicted_draws_fix(g2_bayes, newdata = aids) |>
  group_by(.row, cases) |>
  tidybayes::mean_hdi(
    .prediction, .width = c(0.5,0.9,0.95)
  ) |>
  mutate(contains = cases >= .lower & cases <= .upper) %>%
  group_by(.width) |>
  summarize(
    emp_cov = sum(contains)/n()
  )
# A tibble: 3 × 2
  .width emp_cov
   <dbl>   <dbl>
1   0.5    0.538
2   0.9    1    
3   0.95   1    

Logistic regression

Logistic regression as a GLM

This is another case of a generalized linear model, specifically where the outcome is 0-1 data (i.e. Bernoulli draws),

\[ \begin{aligned} Y_i &\sim \text{Bern}(p_i)\\ \text{logit} \, E(Y_i|\boldsymbol{X}_{i\cdot}) &= \text{logit}(p_i) = \boldsymbol{X}_{i\cdot}\boldsymbol{\beta} \\ \\ E(Y_i) &= p_i \\ Var(Y_i) &= p_i(1-p_i) \\ \\ \text{logit}(p_i) &= \log \frac{p_i}{1-p_i} \\ \text{logit}^{-1}(x) &= \frac{\exp(x)}{1+\exp(x)} = \frac{1}{1+\exp(-x)} \end{aligned} \]

Background

Next we’ll be looking at data on the presence and absence of the short-finned eel (Anguilla australis) at a number of sites in New Zealand.

These data come from

  • Leathwick, J. R., Elith, J., Chadderton, W. L., Rowe, D. and Hastie, T. (2008), Dispersal, disturbance and the contrasting biogeographies of New Zealand’s diadromous and non-diadromous fish species. Journal of Biogeography, 35: 1481–1497.

Species Distribution

Codebook:

  • presence - presence (1) or absence (0) of Anguilla australis at the sampling location

  • SegSumT - Summer air temperature (degrees C)

  • DSDist - Distance to coast (km)

  • DSMaxSlope - Maximum downstream slope (degrees)

  • USRainDays - days per month with rain greater than 25 mm

  • USSlope - average slope in the upstream catchment (degrees)

  • USNative - area with indigenous forest (proportion)

  • DSDam - Presence of known downstream obstructions, mostly dams

  • Method - fishing method (electric, net, spot, trap, or mixture)

  • LocSed - weighted average of proportional cover of bed sediment

    1. mud
    2. sand
    3. fine gravel
    4. coarse gravel
    1. cobble
    2. boulder
    3. bedrock

Data

( anguilla = readRDS("data/anguilla.rds") )
     presence SegSumT   DSDist DSMaxSlope USRainDays USSlope USNative DSDam
1           0    16.0  50.2000       0.57      2.470     9.8     0.81     0
2           1    18.7 132.5300       1.15      1.153     8.3     0.34     0
3           0    18.3 107.4400       0.57      0.847     0.4     0.00     0
4           0    16.7 166.8200       1.72      0.210     0.4     0.22     1
5           1    17.2   3.9500       1.15      1.980    21.9     0.96     0
6           0    15.1  11.1700       1.72      3.300    25.7     1.00     0
7           0    12.7  42.3700       2.86      0.430     9.6     0.09     0
10          1    18.2  94.3960       3.43      0.847    20.5     0.92     0
11          0    14.9  45.7370       2.29      2.249     3.9     0.38     0
12          1    18.3  91.8920       1.72      0.861     6.7     0.58     1
13          1    17.1   6.8000       0.52      0.620     0.7     0.00     0
14          0    13.4 190.3900       3.43      0.770    20.1     0.99     0
15          0    13.1 224.4400       6.84      0.290     9.8     0.98     0
17          0    17.0   1.3800       9.09      1.980    10.5     1.00     0
18          1    18.5   1.8685       1.72      0.847    11.8     0.30     0
19          0    15.7  13.8800       0.57      3.300     2.7     0.29     0
20          0    16.6  28.0200       1.15      0.860    19.0     0.57     0
21          0    14.7  40.0500       0.29      0.310    15.2     0.55     0
22          0    15.7  44.1100       1.15      2.780    26.6     0.99     0
23          1    18.3  81.2550       0.57      0.862     7.9     0.01     0
24          0    14.6   0.4200       0.46      0.340    16.7     0.80     0
25          0    16.7 128.3100      10.76      1.101    12.3     0.70     1
30          0    15.2 310.0100       2.29      1.082     7.6     0.93     1
31          0    13.0 194.9700       4.57      0.240    18.9     0.88     0
32          0    19.1   4.8783       0.57      0.847     0.0     0.00     0
35          0    13.8  14.2100       0.57      0.410    13.6     0.73     0
36          0    17.2 363.0100       4.00      0.974     7.5     0.30     1
37          0    18.8   1.1340       0.57      1.504    19.3     0.80     0
38          0    16.5   4.4000       0.57      1.980    27.4     0.98     0
39          0    17.2  22.5200       1.72      1.300    11.5     0.06     0
40          0    16.5  26.0700      14.04      0.956    23.9     0.93     0
41          0    13.1 300.7600       8.53      0.320    20.9     1.00     1
43          0    16.3  73.8300       0.57      3.270    20.1     0.98     0
44          1    16.2   6.7400       0.34      1.980     0.9     0.17     0
45          0    16.6  16.0880       1.15      2.249     2.5     0.01     0
46          0    15.4  14.7100       1.15      3.300    14.3     0.94     0
47          0    16.4 118.8100       4.57      0.210    21.3     0.75     1
48          1    18.2  94.3960       3.43      0.847    20.5     0.92     0
49          1    18.3  93.0110       0.57      0.874     8.6     0.09     1
50          0    15.0 169.9500       4.00      1.940    27.4     0.98     0
51          0    18.5  60.4550       0.57      0.847     6.0     0.09     0
52          1    19.0   3.0004       1.72      0.847     3.8     0.07     0
53          0    14.9  45.7370       2.29      2.249     3.9     0.38     0
56          0    18.8  10.4850       0.17      1.512     9.3     0.26     0
57          0    17.8 194.1100       1.15      1.396    19.1     0.40     0
59          0    17.1   0.3500      10.76      1.220    23.9     0.96     0
60          0    14.5 142.1900       6.28      1.062     2.4     0.00     1
61          0    16.7  30.8900       2.86      1.220    29.5     0.94     0
62          1    16.9  14.9400       0.57      0.350    10.5     0.11     0
63          0    16.0  89.4500       1.15      3.300    24.4     0.95     0
64          0    14.7 190.0400       4.57      0.280    11.4     0.91     0
65          0    16.9  12.7200       0.17      0.370     0.3     0.02     0
66          0    12.8 264.3800      12.95      0.240    10.6     1.00     1
68          0    16.9  23.6100       0.57      1.210    28.4     0.90     0
69          0    16.8  11.5900       0.40      0.690    19.9     0.71     0
70          0    16.8 173.4400       1.72      0.210    10.1     0.87     1
71          1    18.7   8.1957       1.15      1.153     8.7     0.08     0
72          0    17.8   3.3676       9.09      1.153    24.9     1.00     0
73          0    17.4   1.1900       0.57      1.220    26.2     0.65     0
74          0    13.6 119.0300       4.57      0.290     6.4     0.61     0
75          0    15.8  46.1400       1.15      3.300     7.1     0.58     1
76          0    16.2  85.7600       0.57      3.300     3.5     0.35     0
79          0    16.7 173.8600       1.72      0.210    16.1     0.64     1
80          0    14.3 173.5300       2.86      1.022    12.2     0.99     0
81          1    16.1  79.6800       1.15      0.750     5.7     0.32     0
82          1    16.9 118.3900       5.14      0.647    15.4     0.18     0
83          0    18.6   2.4304       1.72      1.153    14.1     0.08     0
84          0    11.9   6.1800       5.14      0.590    15.9     0.98     0
85          0    17.1  76.9060       5.14      0.846    15.1     0.39     0
87          0    15.1 136.8400       3.43      2.249     2.4     0.31     1
88          0    15.7  26.8700       0.57      3.300    13.3     0.99     0
89          1    18.6   6.2171       1.72      1.153    20.8     1.00     0
90          0    14.4  53.8800       3.43      0.550    23.1     1.00     0
91          1    17.3   4.7100       2.29      1.220    19.9     0.79     0
93          0    19.4   0.3197       2.86      1.074    12.4     0.15     0
94          0    14.7 241.3700       5.14      0.210    19.0     0.89     1
95          0    17.2   7.0200       2.86      0.670    20.8     0.85     0
96          0    15.7   9.5800       0.57      3.260    31.6     0.96     0
97          0    15.0 267.9200       4.00      0.210    24.4     1.00     1
98          0    14.3 233.9500       4.00      0.230    14.6     0.99     1
99          0    13.8   0.0700       2.86      0.930    12.8     1.00     0
101         0    15.9 118.4400       7.41      0.210    15.6     0.08     0
102         0    15.0  25.5000       0.46      3.300     2.2     0.19     0
104         0    15.6 273.6500       3.43      0.250    22.6     0.99     1
105         0    17.0  42.3650       2.86      1.153    11.4     0.06     0
106         0    15.6  13.3000       0.57      3.300    11.1     0.69     0
107         0    15.3  29.9500       1.15      3.300    12.5     0.36     0
108         0    15.0 157.4500       4.57      0.530    20.2     0.97     1
109         0    17.4 219.9400       3.43      0.350    21.1     0.75     1
111         0    16.3 169.7400       2.86      0.762    12.0     0.72     0
113         0    16.5  24.3220       5.71      1.153     8.1     1.00     0
114         0    12.3  42.8500       8.53      0.290     6.4     0.21     1
116         0    18.4   6.2450       3.43      1.514    17.4     0.02     0
117         1    17.3  11.9340       0.57      2.145     3.9     0.04     0
118         0    18.0  72.6900       2.29      0.847    17.3     1.00     0
119         1    18.9  39.4630       0.57      1.445    14.8     0.12     0
120         1    16.1   9.2200       0.40      1.980     0.8     0.25     0
121         0    15.4  13.7400       2.29      3.300    14.9     0.51     0
123         1    17.0   4.4800       0.06      0.390     0.3     0.00     0
124         0    14.3   2.5900       1.72      0.290    12.3     0.56     0
125         1    19.1   1.6088       0.40      0.847     1.5     0.00     0
126         0    15.0  75.1400       1.15      2.570    18.0     1.00     0
127         0    16.5  19.7300       4.00      1.980     9.4     1.00     0
128         0    14.2 236.5300       4.00      0.230    14.3     0.91     1
130         0    15.3 141.5400       4.57      0.210    22.3     1.00     1
131         0    17.9  39.3180       4.00      1.514    23.0     1.00     0
132         0    16.2  82.6000       2.29      1.000    26.0     0.98     0
133         0    15.6  55.1200       5.14      3.300    27.6     0.98     0
134         0    13.5 121.4900       4.57      0.800    24.9     1.00     0
135         1    18.2 117.7700       0.57      0.888     1.1     0.01     0
136         1    18.9 104.1200       0.57      1.145     3.5     0.06     0
137         0    13.6 244.1600       3.43      0.210    13.1     0.98     1
138         1    19.0   0.9870       1.15      0.847     5.9     0.07     1
140         0    15.9 132.3900       5.71      1.143    24.4     1.00     0
141         1    18.1   9.7861       5.14      1.484    14.9     0.28     0
142         0    17.3   6.6800       1.72      1.980    30.4     0.94     0
144         0    13.5 172.1000       3.43      0.650    21.0     0.86     0
147         0    13.4 294.5600       8.53      0.650    18.6     0.84     1
148         0    17.2 297.5900       3.43      0.985    10.6     0.39     1
149         0    16.9   2.3952       1.72      1.465     1.2     0.01     0
150         0    17.1 134.6600       5.71      0.848    16.5     0.99     0
151         0    15.3  31.1900       1.15      0.280    21.7     0.24     0
152         1    18.5  42.7370       1.15      0.847     7.0     0.01     0
153         1    18.4  73.4470       1.15      1.232     9.1     0.11     0
154         1    16.2 155.1900       6.84      1.047    15.0     0.04     0
155         0    18.3 104.0000       0.57      0.881     7.7     0.00     0
156         1    18.7   4.7283       1.15      1.153    14.5     0.34     0
157         1    19.0   3.8395       0.40      0.847     2.3     0.00     0
158         0    16.0  23.0900       0.57      3.160    18.1     0.96     0
159         0    18.8   0.6518       2.29      1.153    14.2     0.97     0
160         0    18.5  81.4620       2.29      1.256    22.8     0.94     0
162         0    16.6  59.0300       1.15      1.980    17.3     0.95     0
163         1    18.4  91.3660       0.57      0.864     6.3     0.01     1
165         0    17.1  25.3800       1.72      1.220    30.1     0.99     0
166         0    15.4  30.3800       0.57      3.300     7.1     0.89     0
167         1    17.9 114.6400       5.71      0.847    20.0     0.91     0
168         0    13.2 221.4800       6.84      0.290    12.8     0.99     0
169         0    15.6  12.0600       0.57      3.300    13.1     0.73     0
170         0    18.4  17.6070       3.43      1.153    15.5     1.00     0
171         0    16.5  83.7620       5.14      0.867    15.2     0.50     0
172         1    18.8   1.0221       0.00      1.514     5.1     0.21     0
174         0    15.7   9.6200       1.15      3.300     8.5     0.99     0
175         0    17.0   3.8343       1.72      0.849    13.0     0.02     0
176         1    18.8   2.4325       1.15      1.153    16.9     0.80     0
177         1    17.2   3.9300       0.57      1.980    26.6     0.96     0
178         0    16.7  54.0200       1.15      1.980    17.8     1.00     0
179         1    17.8 110.7300       3.43      0.926    14.7     0.23     0
180         1    18.1 108.4500       2.29      0.906    11.8     0.00     0
182         0    17.1   0.8400       8.53      1.220    23.4     0.98     0
184         1    17.0 105.9000       0.57      0.638     0.5     0.01     0
185         0    17.2   3.9500       1.15      1.980    16.6     0.91     0
186         0    18.0 104.9500       3.43      0.907    14.1     0.29     0
187         0    18.6  39.2950       0.29      0.994     9.2     0.03     0
189         0    12.1  51.9200      10.76      0.290    12.5     0.91     0
190         1    14.0  13.0100       0.23      0.460     8.4     0.25     0
191         0    17.8 229.4400       1.72      1.350     9.5     0.05     0
192         0    15.1 155.6800       2.29      1.220    16.0     0.94     0
193         0    16.9  11.1170       0.57      0.870    22.3     0.78     0
196         0    11.7 258.3400      13.50      0.210    14.4     1.00     1
197         0    15.2 164.0500       4.57      0.330     3.6     0.91     1
198         0    17.2 310.8200       1.15      1.153    13.6     0.41     0
199         0    15.2  41.1800       2.29      3.300    11.8     0.28     0
200         0    14.5 130.2600       5.14      1.750    13.1     0.99     0
201         0    16.0  66.9400       0.57      0.340    13.1     0.57     0
202         1    14.9  25.2300       1.15      0.290    13.6     0.22     0
203         0    13.4 240.0600       2.86      0.210     5.6     0.88     1
204         0    17.0   6.5700       0.23      1.980    23.0     1.00     0
205         0    19.1   0.8370       1.72      0.996     6.9     0.22     0
206         0    15.0 119.0800       0.57      0.370     0.3     0.00     0
207         0    15.9  18.9400       0.57      3.300    11.1     0.87     0
208         1    16.7   1.6500      12.41      1.980    30.8     0.98     0
211         0    18.0 172.5000       1.72      1.257     6.9     0.01     0
213         0    18.1 160.1600       1.15      0.878     7.9     0.05     0
214         0    18.4  78.6620       0.57      0.847     9.3     0.03     1
215         0    18.3   9.6670       1.72      0.847     9.7     0.15     0
216         0    15.0 271.7500       8.53      0.360    23.5     0.97     1
217         0    14.6 131.2800       5.71      1.230    20.4     0.99     0
218         0    18.4  34.0210       3.43      2.166    13.9     0.49     0
219         0    15.7  56.3700       2.86      1.980    30.1     1.00     0
220         1    18.9 104.2300       0.57      1.147     3.5     0.07     0
221         0    15.7   7.1300       0.34      3.300    14.6     0.60     0
224         1    18.5   7.1514       1.72      1.153    20.7     1.00     0
225         0    13.8 246.1000       5.71      0.210    15.5     0.69     1
228         0    18.6  68.5370       2.29      1.321    13.9     0.82     0
229         0    16.5 317.9200       5.14      1.153    14.8     0.80     0
230         0    18.7  15.6060       0.17      0.872    18.0     0.56     0
231         0    16.9  13.0400       1.15      0.550    26.6     1.00     0
233         0    17.2  34.3600       1.72      1.230    13.9     0.07     0
234         0    14.2 121.7500       2.29      0.380    21.2     0.98     0
235         0    18.2 121.3400       0.57      0.894     1.1     0.02     0
236         0    13.0 299.9100       8.53      0.320    22.1     1.00     1
237         0    17.4  71.7090       2.86      1.461     8.3     0.23     1
238         0    18.6  15.5130       0.57      0.847     9.2     0.21     0
239         0    16.5  37.6700       1.72      0.520    17.3     0.69     0
240         0    12.4  67.8700       6.28      0.290     8.4     0.82     1
241         0    17.9  72.2000       2.29      1.513    19.4     0.40     0
242         0    18.1 122.4200       0.57      0.858     3.0     0.04     0
244         0    17.0   5.2396       0.57      1.975     2.1     0.05     0
245         1    18.1 116.3000       0.57      0.847     0.8     0.03     0
246         0    16.2  52.8600       0.57      2.360    27.1     0.91     0
247         0    12.3  84.7400       4.00      0.740    25.2     0.99     0
248         0    15.8  66.0700       2.29      3.030     7.2     0.91     0
249         0    18.2 111.1900       0.57      0.847     1.0     0.00     0
250         0    17.2   6.2090       0.57      2.249    10.9     0.60     0
251         0    18.2 109.8900       0.57      0.897     0.3     0.00     0
252         0    12.8  92.8100       6.84      0.290    12.9     0.14     0
253         1    17.5   2.8362       0.40      0.584     0.6     0.00     0
254         1    17.2   5.0904       0.52      0.939    13.1     0.18     0
255         1    18.8   3.1752       0.00      1.514     7.8     0.18     0
256         1    17.6  80.3380       7.97      1.167    14.0     0.33     0
257         0    18.7   9.1703       1.15      1.153    18.8     0.96     0
259         0    13.9  25.3800       0.57      0.340     0.3     0.02     0
260         0    15.9  66.3700       0.57      0.340    13.1     0.57     0
262         1    17.6  59.5010       3.43      0.760     8.5     0.04     0
263         1    18.8   1.9007       1.72      1.153    15.3     0.79     0
264         0    15.9  31.6200       1.15      3.300     6.9     0.73     0
265         0    15.4  27.0530       2.29      2.224     2.9     0.26     0
266         1    18.9   4.6465       1.15      0.847     9.3     0.43     0
267         0    15.4  82.9800       0.57      0.340    13.7     0.60     0
268         0    15.7  10.8900       1.15      3.300    14.1     0.80     0
269         0    16.1   5.9400      10.20      1.980    13.3     1.00     0
270         0    14.6  95.9850       6.28      1.127    20.3     1.00     0
271         0    17.1 301.2400       3.43      1.023     3.9     0.06     1
272         0    16.0 156.1800       2.86      0.991    12.4     0.85     0
273         0    14.2  53.7400       1.15      0.410     6.9     0.54     0
275         0    13.7 111.1100       4.00      0.310    23.4     0.96     0
276         0    15.4  84.6700       2.86      1.980    24.2     0.98     0
277         1    18.3  94.5470       0.57      0.876     9.4     0.02     1
278         0    16.5 111.7500       0.50      0.607     9.9     0.05     0
279         0    15.8 101.1100       0.57      3.300     4.2     0.23     0
280         1    15.4  32.4000       0.52      0.290     6.6     0.02     0
281         0    17.2 283.7600       3.43      1.263     8.4     0.15     1
282         1    17.1   8.3400       0.46      0.480    14.0     0.41     0
283         1    18.7   3.2279       5.14      0.847     4.4     0.01     0
286         0    14.8 229.5300       2.29      0.210     1.8     0.00     1
287         1    19.0   9.8590       3.43      1.199    13.8     0.42     0
289         0    15.2   7.1000       1.15      3.300    12.0     0.21     0
290         0    15.4  71.6100       1.72      0.770    25.1     0.88     0
291         0    15.7 122.6500       6.28      1.153    23.8     1.00     0
293         1    16.0  15.6720       1.15      2.232     4.9     0.70     0
294         0    13.3  64.9000       7.41      0.290    21.7     0.07     0
295         0    16.4  14.6570       0.57      2.144     2.5     0.12     0
296         0    13.5 192.9100       4.57      0.230    17.6     0.78     0
297         0    17.7 186.0800       1.72      0.992    12.1     0.65     1
298         0    17.1 375.4700       4.00      1.053     9.4     0.34     1
299         1    15.0   1.0400       0.11      3.300    14.7     0.96     0
300         0    16.4 120.2900       4.57      0.210     5.1     0.17     1
302         0    17.1 212.4200       5.14      1.301     7.4     0.12     1
303         1    17.9 114.6400       5.71      0.847    20.0     0.91     0
305         0    17.6  75.2830       4.57      1.313    19.0     0.98     0
306         0    19.0   1.0367       0.57      0.847     8.4     0.41     0
307         0    17.0   6.2500       0.06      0.390     0.2     0.00     0
308         0    18.0  88.1290       2.29      1.514     7.5     0.07     0
309         0    13.9  22.5000       4.57      1.980    10.7     0.99     0
310         0    18.2  11.2870       5.71      1.141    21.1     0.23     0
312         1    18.2   7.5962       3.43      1.514    18.0     0.96     0
313         0    15.9  18.9400       0.57      3.300    11.1     0.87     0
314         0    16.0 145.9300       4.57      0.300     0.9     1.00     1
315         0    15.2 105.6400       2.29      0.250    13.3     0.15     0
317         0    12.0 274.2300      12.95      0.290    12.8     1.00     1
320         0    16.9  87.0590       2.29      0.771    10.6     0.30     0
321         0    18.9  19.3900       0.57      1.047    16.0     0.48     0
323         1    18.3  93.6860       1.72      0.847    13.4     0.73     0
324         0    12.9  77.0300       6.28      0.290     6.2     0.10     0
325         1    19.0   1.3037       1.72      0.847     5.0     0.35     0
326         0    15.7   6.9400       0.29      1.980    18.1     0.97     0
327         0    15.7 206.9900       3.43      0.210    14.9     0.36     1
329         0    18.4  14.2060       1.15      1.153    17.5     0.80     0
330         0    12.7 268.0800      12.95      0.260    17.2     0.99     1
333         0    12.9  70.0300       4.00      0.360     8.3     0.02     0
334         0    16.5 120.2500       7.97      1.153    27.8     1.00     0
335         0    15.2 135.5600       3.43      2.249     4.3     0.59     1
336         1    18.8 150.1400       1.15      1.153    13.4     0.59     0
337         0    18.4  46.5940       2.29      1.514    14.1     0.00     0
338         0    15.6 146.5200       4.00      1.870    23.1     0.92     0
339         0    14.6 254.5700      12.95      0.210    15.8     1.00     1
340         0    16.8  52.0300       1.15      1.980    20.1     0.99     0
341         1    18.3   9.6670       1.72      0.847     9.7     0.15     0
342         0    18.1  66.6930      10.76      1.464     8.3     0.01     1
343         0    18.8   1.8934       1.15      1.147    19.5     0.98     0
344         0    15.1  48.0000       1.72      2.249     4.2     0.80     0
345         0    14.0   1.8400       0.57      0.290    10.1     0.37     0
346         1    17.6   6.1871       0.40      2.117     3.8     0.03     0
347         0    16.9   5.8100       4.00      1.220    26.5     0.58     0
348         0    15.4   2.2900       0.52      3.300    21.8     0.98     0
349         0    13.8 118.5300       4.57      0.800    23.0     0.99     0
351         0    13.0  22.3800      15.11      1.980    11.0     1.00     0
353         1    19.0   0.7046       2.29      0.847    10.8     0.21     0
354         0    18.3  80.7680       0.57      0.847    13.4     0.09     0
355         0    16.4  30.3750       1.15      0.866    19.7     0.62     0
356         0    15.2 152.3300       2.29      0.834     8.7     0.54     1
358         0    17.2   0.2200       1.15      1.220    19.8     0.99     0
359         0    15.8 110.6300       1.15      0.210    11.3     0.05     0
360         0    15.6  15.5650       4.57      0.882    24.7     1.00     0
361         0    18.1  45.1810       2.86      1.514    13.6     0.03     0
362         0    15.5  96.7700       1.15      0.290    22.3     0.10     0
364         0    17.6  12.1180       0.17      0.584    14.5     0.10     0
365         0    18.9   0.5670       0.40      1.720    29.2     0.92     0
366         0    18.9   2.0309       1.15      0.959     5.9     0.00     0
367         0    16.6 171.1000       1.72      0.210    11.9     0.42     1
369         0    13.5  44.7000       4.57      0.290     8.0     0.27     0
370         0    14.4 107.7100       4.00      1.300    20.8     0.90     1
371         0    17.4  37.8240       1.15      1.751    12.7     0.35     0
372         0    14.3  38.5100       1.72      0.290    22.8     0.11     0
373         0    15.8 197.1600       2.29      0.210    16.0     0.45     1
374         1    18.3  91.9590       1.72      0.863     8.3     0.58     1
375         0    14.0  69.3600       2.86      0.610    28.1     0.95     1
376         0    14.2 250.6900       5.14      0.210    18.3     0.99     1
377         0    18.7   6.7117       0.17      1.514     8.6     0.45     0
378         0    14.1 304.0200       7.41      1.610    26.8     0.99     1
379         0    17.9  49.2630       1.72      1.875    10.8     0.40     0
380         0    19.6   3.1722       2.86      1.153    13.7     1.00     0
381         0    16.1  60.2100      14.57      0.550    25.1     0.83     0
382         0    14.6 323.4100       4.57      1.450    30.8     0.97     1
383         0    16.1 119.1100       7.97      0.210    17.4     0.58     0
384         1    18.7  12.9640       1.15      1.149    16.2     0.73     0
385         0    15.3  12.2200       2.29      3.300    15.3     0.97     0
386         1    17.0  69.9400       0.57      0.775    17.7     0.41     0
387         0    12.0  30.4200      10.76      0.290    16.5     1.00     0
388         1    19.1   0.6343       1.72      0.987     6.8     0.10     0
389         0    14.0 149.3200       4.57      2.400    14.3     0.99     0
391         0    14.5  18.6500      14.04      3.300    31.9     0.98     0
392         0    13.5 132.1800       4.57      0.210    18.0     0.99     1
393         0    17.7  22.9130       2.29      1.509    13.0     0.14     0
394         0    15.7  46.5200       7.97      0.550    13.2     0.12     0
395         0    18.1  23.4870       6.28      1.514    12.1     0.50     1
398         0    17.2   3.9500       1.15      1.980    21.9     0.96     0
399         0    18.6   5.0171       3.43      1.514    23.3     0.00     0
400         0    15.9  73.5700       2.86      0.960    27.4     0.72     0
401         0    15.5  92.1400       1.15      0.330    13.6     0.30     0
402         0    15.4  23.5000       0.57      3.300     3.7     0.85     0
403         1    14.4   4.0600       4.57      0.330    11.4     0.41     0
404         0    10.7  87.4000       6.28      0.330     8.4     1.00     1
405         0    16.9   5.1701       0.57      1.953     3.5     0.05     0
406         0    16.9  79.7400       1.72      1.514    16.9     0.10     0
407         0    14.1   5.8100       1.15      0.330    12.8     0.66     0
408         0    14.4 174.6700       4.57      0.210     7.7     0.03     0
409         0    18.6  28.5690       0.57      1.072    10.4     0.13     0
412         0    13.8 103.7700       4.57      0.290     6.9     0.67     0
413         0    15.9 173.5600       1.72      0.861    21.5     0.71     0
414         0    18.7  11.0490       0.57      1.514    12.9     0.46     0
415         1    17.9  96.9920       2.29      0.874     7.9     0.25     1
416         0    14.4   0.2200       0.57      0.290     8.8     0.04     0
417         0    14.0  83.9300       2.86      0.770    25.8     0.98     0
419         0    18.2   8.1808       3.43      1.514    17.3     0.98     0
420         0    14.2  41.5700       2.29      0.340     5.3     0.01     0
421         0    16.0 118.1500       4.57      0.210    17.6     0.34     0
423         0    17.2  30.9480       2.29      1.505    13.2     0.04     0
425         0    16.2 255.0900       3.43      0.210    20.5     1.00     1
426         1    17.1  14.7000       1.72      0.500    15.9     0.53     0
428         0    14.0  51.1600       2.29      0.410     8.2     0.94     0
430         1    19.1   0.8464       1.15      0.847     6.8     0.04     0
432         0    14.0 251.2000       5.14      0.210    22.1     0.98     1
433         0    19.6   0.6291       1.15      1.153    12.3     0.64     0
434         0    15.6  11.2200       0.57      3.300    10.7     0.67     0
435         0    16.5  17.5400       5.71      1.220    17.3     0.99     0
436         1    18.6  62.3510       0.23      1.091     2.9     0.03     0
438         0    13.8 247.8900       4.00      0.230    23.4     0.95     1
439         0    15.7  15.2900       0.29      3.300     0.6     0.05     0
440         1    16.5  15.1890       2.29      1.830     2.3     0.01     0
441         0    18.7  12.4590       1.72      0.986    15.5     0.50     0
442         0    16.8 167.6700       1.72      0.210    10.1     0.72     1
443         0    13.6 212.3500      11.86      1.160    30.5     0.99     1
445         0    18.9   2.3798       1.72      0.847     9.5     0.72     0
447         0    15.7  97.5800       1.72      1.220    17.2     0.92     0
449         0    12.5 160.5200       5.71      0.210     4.5     1.00     1
450         0    15.8  90.4400       2.86      1.220    25.6     1.00     0
451         0    13.6   0.7200       0.11      0.640     3.8     0.99     0
453         0    15.4  17.8300      16.70      3.300    28.5     0.99     0
454         1    18.9   3.8840       1.15      0.847    13.0     0.04     0
455         0    16.0 123.8000       3.43      2.243     1.3     0.01     1
456         1    18.5   2.2598       2.86      1.143    19.4     0.95     0
457         0    12.5 204.6800      13.50      0.830    18.4     0.99     1
458         0    16.9 143.0000       5.14      0.846    17.3     0.03     0
459         1    17.1  13.9100       0.57      1.980     3.3     0.13     0
460         0    15.1  63.2000       1.15      0.340    18.0     0.72     0
461         1    17.4  75.0640       6.28      1.153    15.3     0.76     0
463         0    18.5   0.1324       6.84      1.067    12.4     0.04     0
465         0    14.0  48.5200       6.28      0.290     6.7     0.11     0
466         0    16.2  14.8900      12.41      0.550    23.8     0.99     0
468         1    17.0   9.2917       0.57      0.882    23.2     0.69     0
469         0    18.2 178.9300       1.72      1.226     6.0     0.04     1
470         0    15.3  33.5800       6.28      3.300    30.2     0.98     0
471         1    14.9  25.5600       1.15      0.290    12.4     0.04     0
472         1    13.6  21.4800       1.15      0.480     8.0     0.27     0
473         0    15.9  35.2800       0.57      3.300    11.6     0.74     0
474         0    18.9   1.4185       0.40      0.887     9.8     0.74     0
475         0    13.8  21.7000       1.15      0.360    11.8     0.22     0
477         0    18.8  61.3620       0.57      1.321    14.0     0.79     0
479         0    15.5  20.8000       7.41      3.300    10.1     0.99     0
480         1    18.1 101.5800       2.29      0.882    15.9     0.99     0
481         0    16.7   1.1300       2.86      1.980    10.8     1.00     0
482         0    14.9  66.1200       0.57      0.340    11.6     0.54     0
485         0    16.4  38.0980       5.14      0.760     5.4     0.03     0
486         1    18.4  76.2360       1.15      1.269     4.2     0.06     0
487         0    16.2 213.0400       4.57      0.280    22.2     0.73     1
489         0    15.0 301.4100       2.86      1.059     9.9     0.87     0
490         1    18.3 114.6300       0.57      0.847    14.2     0.49     0
491         0    16.0 326.2400       7.41      1.153     6.8     0.06     0
492         1    18.7 133.8100       1.15      1.153     5.7     0.11     0
493         0    18.3 106.6100       0.57      0.850     1.1     0.00     0
495         0    16.4  31.3820       1.15      0.866    22.6     0.84     0
496         0    15.9  66.3700       0.57      0.340    13.1     0.57     0
497         0    14.0 120.4000       7.41      1.153    24.7     1.00     0
498         0    15.8  27.1500       2.29      3.300     5.0     0.99     0
499         0    17.3   9.0200       1.72      1.980    17.3     0.78     0
500         0    17.0  36.9200       1.72      1.220    14.4     0.97     0
501         0    15.6  55.1200       5.14      3.300    27.6     0.98     0
502         0    16.2  59.1500       2.29      2.970     9.3     0.93     0
503         1    18.4  58.2220      10.76      1.122     9.3     0.30     1
504         0    16.5   4.6400       0.57      1.980    15.8     0.93     0
505         0    13.7   1.3200       1.15      0.520    18.2     1.00     0
506         0    15.7  35.4000       1.72      0.811    24.3     1.00     0
507         0    17.0  26.6900      13.50      1.220    32.0     0.99     0
508         0    15.6  85.5810       6.28      0.760    23.3     0.91     0
509         0    18.2  30.1240       3.43      2.206    14.5     0.05     0
510         1    18.1  84.9550       1.15      1.189    14.4     0.67     1
511         0    14.2   4.8000       1.72      0.320    11.0     0.71     0
513         0    18.0   8.0029       6.28      1.039    10.2     0.44     0
514         0    16.9  35.8000       1.15      0.550    25.6     0.90     0
515         1    18.4  47.3980       1.15      1.514     9.9     0.00     0
517         0    18.3  68.3380       0.57      1.514    18.1     0.12     0
518         0    17.5 144.1200       0.57      1.505    20.6     0.79     0
519         0    14.0 130.4700      10.20      1.980    29.0     0.99     0
521         0    13.6 218.9500      13.50      0.300    13.4     1.00     1
522         0    15.0 159.6100       2.29      1.220    19.8     0.68     0
523         1    18.5  69.4590       0.17      0.887     4.9     0.05     0
524         0    18.6   6.3290       3.43      1.333    16.8     0.08     0
526         1    18.9   6.0701       1.72      0.847     5.5     0.08     0
527         0    14.4  24.3600       1.15      0.290    10.1     0.01     0
528         1    16.9  15.2700       0.34      0.340     0.1     0.00     0
529         0    15.2  84.8900       1.15      2.680    26.1     1.00     0
530         0    15.6   2.7200       2.29      3.300    14.4     1.00     0
533         0    13.9 208.6200       5.14      0.970    18.6     1.00     1
534         0    17.0  75.8800       6.84      1.514    23.4     0.61     0
535         0    17.7  89.8280       0.57      0.584    20.7     0.60     0
536         0    16.4  97.7730       6.28      1.514    24.6     0.81     0
537         1    17.1  23.3600       0.57      0.966    24.3     0.86     0
538         0    14.7  89.9290      12.41      1.646    22.4     1.00     0
540         1    18.7  14.4930       0.34      1.153    10.5     0.24     0
541         1    17.2  62.2350       0.57      0.769    17.3     0.37     0
542         0    18.4  26.5370       2.86      1.514    15.0     0.09     0
543         1    18.9   4.5162       1.15      0.847     7.8     0.18     0
544         0    15.3  23.0370       1.72      2.234     6.7     0.76     0
545         0    19.3   2.7552       1.72      1.153    16.0     0.83     0
547         0    14.0 108.9100       2.29      0.350     6.4     0.14     0
548         1    16.3 110.9200       3.43      1.705     6.3     0.01     1
549         1    19.0   2.2907       2.29      0.854     6.8     0.33     0
550         0    16.9   3.7500       2.29      0.970    28.5     0.99     0
551         0    14.7 296.8100       3.43      1.190    23.7     0.73     1
552         0    18.9   1.8955       1.15      0.999     4.9     0.01     0
553         0    14.9  44.1100       7.41      1.980    29.0     1.00     0
554         1    17.9 185.5300       1.72      1.381    12.5     0.45     0
555         1    18.7  17.8200       0.57      0.847     2.0     0.00     0
556         0    18.2  95.0090       2.29      0.850    17.6     0.89     0
557         0    18.8  33.8900       0.06      1.015     0.1     0.50     0
558         0    15.7   2.6500       1.15      2.810    28.4     1.00     0
559         0    15.4 108.1900       1.15      2.250    10.3     0.81     0
560         0    12.3  57.2900       5.14      0.290     8.5     0.98     0
561         0    13.5  12.8100      15.11      1.980    18.2     0.99     0
563         0    19.0   4.9529       0.57      0.847     5.0     0.14     0
566         0    15.8 110.0500       1.15      0.220    11.2     0.07     0
570         1    17.7 184.2100       1.15      1.435     8.3     0.16     0
571         0    19.6   2.0712       1.72      1.153    10.2     0.91     0
572         1    17.2   1.2400       0.46      0.480    13.9     0.40     0
574         0    16.2 271.9300       3.43      0.560    27.2     0.95     1
577         0    16.8 251.4400       4.00      1.156     5.1     0.09     0
578         0    15.1 118.3700       3.43      2.330    19.4     0.99     0
579         0    17.7  97.9260       2.86      0.847    16.7     0.88     1
580         1    18.3  30.9430       0.57      1.514    26.3     1.00     0
581         0    17.9  17.6430       5.14      1.153    12.3     0.98     0
584         1    19.0   1.5012       0.57      0.847     8.8     0.62     0
585         0    18.6  17.4270       0.57      0.847     2.2     0.04     0
586         1    18.7   5.5829       0.57      0.847     2.3     0.01     0
588         0    16.0 116.9300       4.57      0.210    10.8     0.90     1
589         0    17.1  36.2600       1.72      1.230    13.4     0.07     0
590         1    18.7  21.3890       1.15      2.249    12.2     0.38     0
591         0    15.4 171.7100       7.97      0.976    24.6     0.99     0
592         0    16.3  65.7900       5.71      1.980    16.3     0.99     0
593         0    15.5 305.4100       2.29      1.100     3.6     0.16     1
594         0    15.8  28.4600       0.57      3.300    16.4     0.68     0
595         0    13.0  22.2700      15.11      1.980    10.8     1.00     0
596         0    16.1  26.1000       1.72      3.120    22.2     0.93     0
597         1    18.7  17.1540       0.46      0.760     2.0     0.01     0
598         0    13.6 119.4700       4.57      0.290     6.4     0.61     0
599         0    15.2  27.3700       2.86      3.300    11.7     0.62     0
600         0    13.6 208.1800       6.28      2.700    31.0     0.94     1
601         1    18.4  75.5320       1.15      1.205     9.7     0.24     0
602         0    18.6  24.6670       1.72      2.135     5.3     0.48     0
603         0    16.6   1.3600       4.57      1.220    26.6     0.96     0
604         0    19.3   0.2349       2.86      1.071    11.0     0.85     0
605         0    13.8 150.8000       4.57      2.930    30.9     0.99     0
606         0    18.7   1.6834       2.29      1.153    14.0     0.00     0
607         0    15.9 271.1600       7.41      0.290    28.9     0.96     1
608         0    17.3  40.9200       0.11      0.929    25.6     0.81     0
610         1    16.8   2.5900       1.15      0.550    16.0     0.16     0
611         0    16.8  44.3000       2.29      1.220    27.6     0.61     0
612         0    16.3 114.8100       6.28      1.153    20.2     0.72     0
613         0    15.4  65.9500       1.72      3.300    28.6     0.99     1
614         0    16.9   1.1500       1.15      1.220    21.6     0.73     0
615         1    16.9   4.1189       1.72      0.912    15.0     0.07     0
616         1    17.2   4.6700       0.46      0.480    14.0     0.41     0
618         0    13.7 112.5200       5.14      0.310    18.9     0.87     0
619         0    18.3  34.4670       0.57      1.514    20.7     1.00     0
620         0    16.4 252.2900       3.43      1.153     9.1     0.50     0
621         0    13.8  13.1000       0.57      0.410    11.2     0.39     0
624         0    18.1  73.2040       2.29      1.193    14.1     0.42     0
625         0    12.8  92.8100       6.84      0.290    12.9     0.14     0
626         0    16.9  91.0530       0.57      0.673     0.5     0.00     0
627         1    18.7   4.6126       4.00      1.153    16.0     0.97     0
631         0    17.4   6.4300       1.15      1.220    22.6     0.08     0
632         0    18.2   2.7749       5.14      1.153    24.4     0.90     0
634         1    16.6  27.3700       0.40      0.720    21.5     0.81     0
635         0    14.1 250.6200       5.14      0.210    17.2     0.99     1
636         1    17.0  26.8320       0.57      2.215     3.6     0.03     0
637         0    15.0 301.4100       2.86      1.059     9.9     0.87     0
638         0    19.3   2.1107       6.28      1.153    20.1     1.00     0
639         1    18.5  10.8980       1.72      1.514    20.1     0.92     0
640         1    17.2   4.6700       0.46      0.480    14.0     0.41     0
643         1    18.3 189.3800       0.57      1.161     6.8     0.10     0
644         0    18.4  47.3980       1.15      1.514     9.9     0.00     0
645         1    18.6   9.8402       1.15      0.847     6.7     0.63     0
646         0    19.1   1.0264       2.29      0.847     6.7     0.28     0
647         1    18.0 184.8600       1.15      1.374    12.2     0.33     0
648         0    13.6   1.1600      18.78      1.000    30.3     1.00     0
649         0    14.1  63.3100       2.29      0.290    23.8     0.38     0
650         0    16.9   7.9254       4.57      0.852    28.4     0.99     0
651         1    18.1  77.1080       2.29      1.425    13.8     0.23     0
652         0    17.5   5.4526       5.71      1.145    16.7     1.00     0
653         1    17.1   4.2400       0.57      0.550    15.0     0.31     0
654         0    18.6  10.6560       2.86      1.153    15.8     0.82     0
655         0    15.0 101.3500       7.41      2.070    16.6     1.00     0
656         0    18.1   6.3714      10.20      1.514    28.9     1.00     0
657         0    13.8   0.3400       6.28      0.790    26.4     0.99     0
658         0    12.3 125.2700       4.57      0.800    26.1     0.99     0
659         0    18.3  49.3060       0.57      1.514    21.1     0.92     0
661         0    16.4  27.1700       3.43      1.220    24.8     0.00     0
662         1    16.0 108.1000       2.86      0.841    25.3     1.00     0
663         0    15.7 206.1300       3.43      0.210    20.1     0.90     1
664         1    18.8   6.3662       0.52      1.514    24.6     0.78     0
666         1    18.7   5.8396       1.15      0.847     7.3     0.52     0
667         0    15.5  91.7090       5.14      0.886    12.2     0.59     0
668         0    18.7   6.4987       0.57      0.995    13.7     0.00     0
670         0    18.5   1.2861       2.29      1.457    19.4     0.76     0
671         0    16.1  28.6900       0.57      3.260    10.3     0.67     0
672         0    14.0  12.2900      15.11      1.980    12.6     0.98     0
673         0    15.5 145.8200       4.00      1.870    23.1     0.92     0
674         0    17.7  26.9400       2.86      1.514    15.7     0.43     0
675         0    16.7   2.4800      14.57      1.980    22.0     0.99     0
676         1    17.8   8.3239       0.57      0.805    17.7     0.49     0
677         0    13.6 169.2000       3.43      0.640    20.7     0.86     0
678         0    15.7 217.4500       1.72      0.210    18.5     0.76     1
679         0    16.4  93.2220       3.43      1.424    15.5     0.14     1
680         1    16.5  99.7190       2.86      0.822    24.5     0.80     0
681         1    19.6  13.9050       0.57      1.153     8.9     0.17     0
683         1    18.0  91.4370       1.72      0.850    14.9     0.75     0
684         0    13.9 244.6400       5.14      0.210     9.7     1.00     1
685         0    13.7 222.5800       4.57      0.210    22.0     0.76     0
687         0    18.2  87.7100       3.43      1.396    18.3     0.70     0
689         0    16.1  24.4170       2.29      1.966     1.9     0.01     0
690         0    18.7   1.6834       2.29      1.153    14.0     0.00     0
691         1    18.7  21.2430       0.57      0.847     2.0     0.02     0
692         0    15.3 157.8700       4.00      1.940    22.8     0.99     0
693         1    18.5  68.9450       0.17      0.887     4.8     0.05     0
694         1    17.7  25.8620       0.57      0.584    12.3     0.16     0
696         0    15.1  28.8800       0.57      0.290    19.5     0.24     0
697         0    16.9  78.8700       6.84      1.514    24.7     0.66     0
699         0    17.0  89.5670       6.28      1.514    21.9     0.60     0
700         0    16.5 244.4000       3.43      1.207     7.6     0.10     0
701         0    13.3  60.1100       7.41      0.290    17.9     0.08     0
702         0    16.6   5.2400       9.09      1.980    22.3     0.99     0
703         0    14.4   4.3700       0.40      0.290    13.0     0.30     0
704         0    16.9  78.3180       6.84      1.514    21.2     0.55     0
705         0    15.4  15.0230      11.86      0.881    22.9     0.99     0
706         0    13.9  37.9300       4.57      0.290    24.9     0.28     0
708         1    17.4  25.8700       0.57      0.550    16.4     0.09     0
709         0    16.8  38.1100       3.43      1.220    20.0     0.68     0
710         0    14.0  20.6500       0.57      0.450     9.5     0.79     0
711         0    17.1  25.0100       1.72      1.630    24.9     0.73     0
712         0    16.0  32.2600       0.57      3.270     9.8     0.61     0
713         0    15.9   4.7900       5.14      2.730    20.0     0.89     0
715         1    18.7  18.4350       2.29      1.153    14.9     0.84     0
716         0    16.9  40.4240       2.86      1.153    11.8     1.00     0
717         0    16.1  55.9400       1.72      0.540    15.7     0.62     0
718         0    17.2  15.0040       1.15      2.198     3.0     0.05     0
719         0    18.2  49.8990       1.15      1.514    15.1     0.46     0
720         0    19.4   2.2079       0.57      0.850    11.3     1.00     0
721         1    18.1  13.9010       5.14      0.847     7.8     0.11     0
722         0    16.0  42.8460       1.72      2.249     8.7     0.59     0
723         1    17.3  40.9200       0.11      0.929    25.6     0.81     0
724         0    15.9   7.9700       0.57      0.290     4.4     0.00     0
726         0    15.9  17.0500       0.57      2.840    18.4     0.82     0
727         0    15.2 149.3100       5.14      0.823    22.2     0.59     0
728         0    15.7 118.0000       6.28      1.111    22.9     0.99     0
729         0    16.5  42.0520       5.14      1.153    12.6     0.08     0
730         0    14.1 181.0500       4.00      1.970    28.8     0.99     0
731         0    15.2  16.7600       1.72      0.290     8.4     0.01     0
734         0    17.6  44.0470       3.43      1.567    29.7     1.00     0
735         0    14.0  94.8900       4.57      0.290     7.5     0.60     0
736         1    16.9   2.1900       5.71      1.980    11.4     1.00     0
737         0    16.1  10.5800       1.82      0.530    17.9     0.35     0
738         0    16.5 145.6100       1.72      0.210    18.2     0.44     1
739         0    16.5 213.4200       4.57      0.270    22.6     0.65     1
740         0    16.3  99.5360       2.86      0.781     8.4     0.00     0
741         1    18.9   7.7917       1.72      0.847     3.8     0.06     0
742         1    19.0   6.1147       2.29      1.045    18.7     0.84     0
743         0    18.1  75.8090      10.76      1.274    24.6     0.90     1
745         0    12.5  95.6500       8.53      0.300     8.0     0.77     0
747         0    18.8   0.6394       0.23      1.513    22.8     0.95     0
749         0    18.4  91.3660       0.57      0.864     6.3     0.01     1
750         0    19.0   1.0367       0.57      0.847     8.4     0.41     0
751         0    11.9  38.4700       7.97      0.290     8.1     0.00     0
752         0    14.9  27.0610       2.29      2.247    11.8     0.92     0
753         0    14.3  51.2900       4.00      0.350    10.2     0.02     0
754         0    18.1 148.5900       0.57      1.217    14.8     0.79     0
755         0    17.3   1.6800       1.15      1.980    24.3     0.84     0
756         0    15.4  70.9900       9.65      3.300    21.8     0.90     1
757         0    15.1 108.6800       4.00      0.900    31.4     0.98     1
758         1    18.9   7.9502       0.52      0.847     5.5     0.17     0
759         0    15.6  33.0500       0.57      3.250    14.6     0.81     0
760         1    17.5 215.0600       6.28      1.362    18.1     0.26     0
761         0    14.9  45.7370       2.29      2.249     3.9     0.38     0
762         0    15.6  15.0700       3.43      3.300    11.3     0.86     0
763         0    15.7  58.2300       2.29      3.300    15.3     0.77     1
764         0    15.2  41.1800       2.29      3.300    11.8     0.28     0
765         0    18.6   6.8587       1.72      0.847     4.3     0.08     0
766         0    17.2  36.5780       6.28      1.514     7.4     0.16     1
767         0    18.8  44.4420       0.57      1.153     8.1     0.12     0
768         0    15.6  12.0600       0.57      3.300    13.1     0.73     0
769         0    16.8   9.0666       1.72      0.976    18.6     1.00     0
771         1    18.4  74.0130       1.15      1.221     8.3     0.18     0
772         0    15.9 192.1900       1.72      0.210    18.3     0.00     1
773         0    15.8  28.3000       6.84      3.300    31.8     1.00     0
774         0    16.7  48.3900       1.72      1.850    28.6     0.92     0
775         0    16.6  63.1500       1.72      1.820    28.7     0.90     0
777         0    17.0   5.4200       0.57      0.650    31.1     0.77     0
779         0    14.8 135.3800       6.28      1.070    11.0     0.53     1
780         0    18.9   0.9818       1.15      1.153    18.4     0.55     0
781         0    16.1 110.9200       6.28      1.153    24.4     0.99     0
782         1    18.9   1.3564       1.15      0.847     4.3     0.26     0
783         1    18.0 184.8600       1.15      1.374    12.2     0.33     0
784         0    15.4 103.9500       2.29      3.300    14.3     0.94     0
785         0    12.8  47.2200       6.28      0.290     4.8     0.09     1
786         0    15.6  33.0500       0.57      3.250    14.6     0.81     0
788         0    15.7  20.2000       5.14      3.190    18.1     0.98     0
789         0    15.6   3.5395      11.31      0.859    27.4     1.00     0
790         0    18.3  29.8910       1.72      0.847     9.4     0.08     0
791         1    18.4  74.0130       1.15      1.221     8.3     0.18     0
792         0    16.0   5.0800       6.28      0.550    20.6     0.41     0
793         0    18.5  62.6400       0.57      0.847     9.4     0.11     0
794         0    17.2 202.0900       3.43      0.210    19.5     0.91     1
795         0    18.4  45.0510       0.57      1.514    18.7     0.60     0
796         0    14.7 179.4200       4.57      0.380    13.6     0.83     1
797         0    16.5 278.2400       9.09      1.270    23.1     0.98     1
798         0    12.6 157.4900       5.71      0.220     2.4     0.88     1
799         0    18.2  33.7110       3.43      1.514    18.9     1.00     0
800         0    14.5 318.2600       7.41      2.590    32.6     0.99     1
801         1    18.5  77.4060       4.00      1.183    19.1     0.45     0
802         0    15.7 101.6200       4.00      1.040    27.1     0.96     1
804         0    16.2  52.8600       0.57      2.360    27.1     0.91     0
805         0    16.5   0.6900       2.86      1.220    22.4     0.99     0
806         1    16.9   2.2400       0.57      1.980     9.8     0.11     0
807         0    14.6  77.9300       4.00      3.300    33.5     0.98     0
808         0    15.9 174.9600       5.14      0.881    22.4     0.46     0
809         0    18.6  11.7570       1.15      2.249    18.7     0.64     0
810         0    18.6  11.0250       1.15      0.847     1.8     0.01     0
811         0    15.1  24.8800       0.57      0.290     8.9     0.04     0
812         0    17.9 122.9500       3.43      1.027    14.0     0.81     0
813         1    18.1 110.7100       0.57      0.847     1.2     0.00     0
814         0    18.8   6.4493       0.00      1.514     8.3     0.54     0
815         0    18.4   2.4728       2.29      1.118    18.4     0.97     0
816         0    17.4  69.0540       2.86      1.514     3.4     0.27     1
817         0    14.9  96.7400       0.57      0.380    10.2     0.05     0
818         0    14.2   9.2200       0.57      0.290    21.3     0.38     0
819         0    15.5 152.5700       4.57      0.640    22.2     0.97     1
820         0    15.9 111.9600       6.28      1.153    26.2     1.00     0
821         1    17.9 195.4600       1.15      1.450    19.5     0.61     0
822         0    13.4 298.0000       8.53      0.350    22.7     1.00     1
823         0    17.6 291.2600       1.15      1.159    13.5     0.93     0
824         0    17.2   1.3900       1.72      1.220    22.1     0.98     0
825         1    18.3  57.8020       1.15      1.003    13.7     0.56     0
826         0    16.3 135.2700       4.57      0.280     1.5     0.97     1
827         0    18.9   1.4185       0.40      0.887     9.8     0.74     0
828         0    15.2 188.4800       6.28      1.870    31.1     0.98     1
829         0    15.7  43.3600       2.86      2.760    14.3     1.00     0
830         0    18.2  10.9350       6.84      1.153    14.3     1.00     0
831         0    16.0  69.0000       0.57      0.340    13.1     0.58     0
833         0    17.8  77.0110       2.29      0.847    18.1     0.99     0
834         0    15.3  11.5800       2.86      3.300    15.6     0.82     0
836         0    18.6  35.9030       4.00      1.153     5.0     0.59     0
838         0    15.4  11.7600       4.57      3.300    10.9     0.86     0
839         0    15.8   7.3700       0.40      0.290     0.9     0.00     0
841         0    15.5  54.0000       1.15      2.530     2.6     0.45     0
842         0    14.2 330.3100      10.20      1.840    24.6     0.99     1
843         0    15.0  18.6800       6.84      3.300    23.2     1.00     0
844         0    15.4  12.8800       4.57      3.300    14.4     0.78     0
845         0    15.9   3.7700       2.29      2.590    18.7     0.96     0
846         1    17.1   8.2600       0.34      1.980    12.2     0.63     0
847         0    18.0  24.3890       0.17      0.601    19.5     0.16     0
849         0    14.8  60.9800       7.97      0.490    12.8     0.13     0
850         0    13.9 243.4600       5.14      0.210    25.5     0.99     1
851         0    18.7   4.5753       0.57      0.847     5.4     0.10     0
853         1    16.7  17.9440       1.15      2.249    12.3     0.57     0
854         1    18.7  20.9520       4.00      1.045    17.5     1.00     0
855         0    16.5  64.4300       0.46      0.600     5.2     0.12     0
857         0    15.2   8.4500       0.34      3.300     3.8     0.97     0
860         0    13.5  19.8300       1.15      0.830    27.2     0.89     0
862         0    18.3  34.7330       4.00      2.177    14.1     0.26     0
863         0    17.0   5.0700       0.52      1.980    18.3     0.99     0
864         0    15.5  26.9870       1.72      2.249     2.6     0.48     0
865         0    17.1  28.6350       8.53      1.514    13.8     0.01     0
866         0    17.3 204.4500       1.72      1.514    16.9     0.54     0
867         0    18.2 206.6400       0.57      1.153     9.6     0.23     0
868         0    18.8   4.0404       0.40      1.514     3.9     0.45     0
869         0    18.5  35.6730       1.15      1.514    20.7     0.30     0
871         0    16.8 243.7100       3.43      0.210    18.1     0.99     1
872         0    16.7   1.6500      12.41      1.980    30.8     0.98     0
873         0    16.0  53.5700       1.15      2.740    15.8     0.87     0
875         0    15.1  93.4700       2.29      0.350    13.9     0.60     0
877         0    19.3   2.3155       1.72      1.153    14.3     0.84     0
878         1    17.0   3.7735       0.57      0.913    17.8     0.29     0
879         0    17.5  22.2400       2.29      1.220    20.6     0.16     0
880         0    15.1  28.5770       2.29      2.249     2.9     0.36     0
882         0    17.2  40.7330       3.43      0.875    20.7     0.56     0
883         0    17.8  71.2230       4.57      0.723    21.8     0.67     0
884         0    17.3 268.6100       3.43      1.037    13.5     0.00     1
885         0    15.6 147.4300       6.28      0.210    19.5     0.62     1
886         0    15.8 157.7000       5.14      0.787    25.3     0.81     0
888         0    17.2  10.0820       9.09      0.847     7.8     1.00     1
890         0    12.7  41.8900       6.28      0.290     9.6     0.00     1
891         1    18.8  13.9060       0.52      0.847     8.5     0.17     0
892         1    18.7  17.4230       1.15      0.847     4.2     0.00     0
893         0    17.0   5.4200       0.57      0.650    31.1     0.77     0
894         0    15.3   5.7700       0.57      3.300    14.4     0.44     0
896         0    14.0 130.3400       5.14      2.040    29.0     0.99     0
897         0    17.2   1.5800       1.72      1.220    23.4     0.63     0
898         0    17.5  28.0240       4.00      1.688    22.5     0.99     0
899         0    15.3  83.4000       1.15      0.340    11.1     0.61     0
901         0    15.9  64.9300       0.57      0.680    11.4     0.58     0
902         0    15.3  73.4200       1.72      0.770    25.4     0.89     0
903         1    19.5  12.6920       1.15      1.153    11.5     0.23     0
905         0    16.2 271.9300       3.43      0.560    27.2     0.95     1
906         0    13.6 192.2200       4.57      0.230    17.5     0.69     0
907         0    17.0 101.9000       6.28      1.153    13.8     0.16     0
908         1    15.1  27.2300       0.52      0.290     6.6     0.01     0
909         0    16.2  30.8080       1.15      0.976    21.7     0.99     1
910         0    14.7 129.6400       4.00      0.270     9.7     0.29     0
911         0    16.0  70.1500       0.57      0.340    13.1     0.57     0
912         0    16.9 279.3700       1.72      1.095     9.5     0.75     0
913         0    13.0  21.4500      15.11      1.980     8.5     1.00     0
914         0    16.2 125.9500       2.29      0.758    16.3     0.76     0
916         0    16.2 123.9400       6.28      1.149    16.4     0.40     0
917         0    18.6   4.3610       2.29      1.153    14.9     1.00     0
918         0    12.1 257.7700       6.84      0.210     4.6     0.99     0
919         0    15.4 162.1700       4.57      0.490    10.8     0.32     1
920         0    15.9  54.7170       5.14      0.911    17.4     1.00     0
921         0    16.1   1.1500       0.00      0.290     1.9     0.00     0
923         0    14.8  59.2700       2.29      0.550    21.2     1.00     0
924         1    18.4  77.9220       0.57      0.847     4.6     0.02     1
926         0    17.5  31.5670       4.00      1.514    10.6     1.00     0
927         0    18.1 140.8100       0.57      0.848     7.1     0.13     0
928         0    19.3   4.9601       0.57      0.850     7.9     0.47     0
929         0    14.1  96.7300       4.00      0.800    25.1     1.00     0
930         1    17.6   4.1665       0.57      1.710     3.1     0.05     0
931         0    14.7  31.9050       2.86      2.249     3.8     0.84     0
932         0    17.4  72.5030       0.00      0.584     0.3     0.00     0
933         0    16.1 197.3700       1.72      0.210     4.4     0.00     1
934         0    16.5  25.8000       0.34      2.360    27.1     0.88     0
935         0    14.4 175.3400       4.57      0.240    16.9     0.39     0
936         1    17.0   3.7735       0.57      0.913    17.8     0.29     0
937         1    18.2  63.3540       2.86      1.288     9.2     0.22     0
938         0    17.4  17.7900       0.57      1.220    25.1     0.39     0
939         1    17.1   8.3400       0.46      0.480    14.0     0.41     0
940         0    13.0 261.9900      12.95      0.240    19.9     0.98     1
941         1    17.0  20.9980       0.57      0.975    22.6     0.87     0
942         1    19.4  11.3910       0.57      1.153     8.0     0.35     0
943         0    18.7   8.5575       1.15      0.847    10.8     0.84     0
945         0    15.1   3.3400       1.72      3.300    17.4     0.99     0
946         0    17.0  92.4510       0.50      0.603     8.2     0.04     0
947         0    12.8 151.6900       4.57      0.980    30.9     0.99     0
948         1    16.8  31.1300       0.17      0.340     0.2     0.06     0
949         0    17.3   4.1759       1.72      2.249     4.3     0.00     0
950         1    16.9 138.5300       5.14      0.847    16.8     0.11     0
951         0    17.9 199.6700       1.15      1.454    15.5     0.29     0
953         0    14.5  20.1800       0.57      0.290     8.4     0.14     0
954         0    14.5 133.0600       6.28      1.410    16.6     1.00     0
956         0    12.2 159.2800       5.71      0.260     8.7     0.94     1
958         0    15.4  27.0530       2.29      2.224     2.9     0.26     0
959         0    13.9  92.6300       4.57      0.290     6.9     0.15     0
960         0    14.8 149.4200       9.09      0.848    26.5     1.00     0
961         0    18.3  20.2020       1.72      1.153    17.3     0.68     0
962         0    12.8  90.4600       6.84      0.290    11.4     0.26     0
963         0    16.5 222.4400       5.14      0.888    11.3     0.14     0
966         0    16.1   0.8400       0.00      0.290     0.3     0.00     0
968         0    15.4  13.1300       0.57      3.300    11.3     0.87     0
969         0    15.4  34.2600       2.29      3.300    16.9     0.96     0
970         0    17.5  29.4800      12.95      0.847    12.6     0.19     1
971         0    14.6   0.4200       0.46      0.340    16.7     0.80     0
972         0    16.0  36.3300       1.15      2.840    23.4     0.96     0
973         0    17.7 188.2800       1.15      1.377    12.6     0.45     0
975         0    17.9   7.4454       4.57      1.496    12.8     0.32     0
976         0    15.8  88.8000       3.43      2.810    25.4     0.92     0
977         0    16.2  76.9400       2.86      3.300     9.0     0.95     0
978         0    14.7  52.2700       3.43      0.550    23.2     1.00     0
979         0    15.3  27.3600       9.65      3.300    14.9     0.99     0
980         0    14.4  14.7400       0.29      0.290     9.6     0.09     0
981         0    13.6 250.8000       4.00      0.230    25.9     0.97     1
983         1    18.9   2.2285       0.57      0.847     3.1     0.01     0
984         0    18.8   4.0868       0.57      1.003    15.8     0.00     0
985         0    14.1 243.8600       4.00      0.240    24.4     0.90     1
986         0    17.0  33.2400       1.15      1.220    22.5     0.77     0
988         0    14.9 308.2200      20.30      1.540    30.5     0.82     1
989         0    17.0  42.8290       9.09      1.153    15.3     0.64     0
990         0    15.6  12.6000       1.15      3.300    13.7     0.97     0
991         0    15.1  14.2300       1.15      3.300    12.5     0.73     0
992         1    19.6   0.6291       1.15      1.153    12.3     0.64     0
993         0    14.9  26.5200       2.86      3.300    26.8     0.95     0
994         0    17.2  23.6260       2.29      2.249    16.9     0.50     0
995         0    18.1  24.8250       2.29      1.514     7.7     0.46     1
996         0    13.5 126.7500       6.28      0.290    15.6     0.85     0
997         0    13.7  74.4100       3.43      0.760    29.1     0.99     0
998         0    15.2 105.6400       2.29      0.250    13.3     0.15     0
999         0    18.4  48.3960       2.29      0.847     5.3     0.17     0
1000        0    14.7  37.1500       0.29      0.310    14.5     0.43     0
       Method LocSed
1    electric    4.8
2    electric    2.0
3         spo    1.0
4    electric    4.0
5    electric    4.7
6    electric    4.5
7    electric    4.3
10   electric    3.6
11   electric    3.7
12   electric    1.0
13   electric    3.4
14   electric    4.6
15   electric    5.2
17   electric    4.9
18       trap    1.9
19    mixture    2.8
20   electric    4.2
21   electric    4.4
22   electric    4.8
23   electric    1.0
24   electric    3.3
25   electric    3.7
30   electric    3.5
31   electric    5.8
32    mixture    1.0
35   electric    4.1
36   electric    3.5
37       trap    3.0
38        spo    4.1
39   electric    1.8
40   electric    5.0
41   electric    2.8
43   electric    4.7
44   electric    4.5
45   electric    4.5
46   electric    4.9
47   electric    3.5
48   electric    1.6
49   electric    1.0
50   electric    3.9
51        net    1.0
52   electric    2.2
53        spo    3.6
56   electric    1.9
57   electric    3.4
59        spo    4.4
60   electric    2.0
61   electric    5.5
62   electric    1.0
63   electric    3.8
64   electric    3.4
65   electric    3.1
66   electric    3.3
68   electric    3.2
69   electric    3.0
70   electric    4.6
71   electric    2.1
72   electric    4.5
73   electric    4.2
74   electric    4.7
75   electric    5.2
76   electric    4.7
79   electric    4.9
80   electric    5.7
81   electric    2.0
82   electric    3.8
83   electric    4.0
84    mixture    3.9
85   electric    4.1
87        spo    5.0
88   electric    5.6
89   electric    4.6
90   electric    4.7
91   electric    3.5
93    mixture    1.0
94   electric    3.8
95   electric    4.2
96   electric    4.4
97   electric    3.6
98   electric    5.0
99        spo    3.0
101  electric    1.8
102  electric    4.2
104  electric    4.2
105  electric    4.0
106  electric    4.2
107  electric    3.8
108  electric    4.5
109  electric    3.8
111  electric    5.2
113  electric    6.0
114  electric    3.7
116  electric    3.4
117  electric    4.3
118  electric    3.0
119  electric    2.4
120       net    2.6
121  electric    5.1
123  electric    1.3
124      trap    4.6
125  electric    4.0
126  electric    5.5
127       spo    4.1
128  electric    4.5
130  electric    4.2
131  electric    4.6
132  electric    4.2
133  electric    4.8
134  electric    4.7
135      trap    1.9
136      trap    1.0
137  electric    4.7
138  electric    1.4
140  electric    4.0
141  electric    4.5
142  electric    5.0
144  electric    4.0
147  electric    3.9
148   mixture    1.8
149      trap    1.0
150  electric    4.7
151  electric    5.2
152  electric    5.0
153  electric    3.2
154  electric    2.5
155      trap    1.3
156  electric    2.2
157  electric    1.0
158  electric    4.6
159  electric    2.2
160  electric    5.2
162  electric    6.5
163  electric    1.2
165  electric    4.6
166  electric    4.0
167  electric    5.6
168  electric    5.0
169  electric    4.0
170  electric    4.0
171  electric    4.5
172       net    1.2
174  electric    4.5
175      trap    3.4
176  electric    3.5
177  electric    4.0
178  electric    6.9
179  electric    4.7
180  electric    3.0
182  electric    2.8
184  electric    3.5
185       spo    4.0
186       net    3.5
187       spo    1.4
189  electric    4.2
190  electric    2.9
191       net    4.0
192  electric    4.5
193  electric    4.8
196  electric    4.3
197  electric    3.6
198  electric    4.7
199  electric    4.4
200  electric    6.2
201  electric    4.3
202  electric    6.5
203  electric    6.5
204  electric    4.2
205   mixture    1.0
206  electric    3.7
207  electric    4.0
208  electric    1.1
211  electric    1.2
213   mixture    5.0
214       net    1.0
215  electric    2.8
216  electric    4.0
217  electric    4.7
218  electric    3.9
219  electric    4.0
220  electric    3.8
221      trap    1.5
224  electric    4.4
225  electric    3.8
228  electric    4.7
229  electric    5.0
230  electric    4.2
231  electric    4.2
233  electric    4.0
234  electric    4.5
235      trap    2.0
236  electric    4.6
237  electric    3.0
238       net    1.9
239  electric    4.0
240  electric    5.5
241  electric    5.2
242      trap    1.8
244       spo    2.6
245  electric    1.4
246  electric    6.0
247  electric    4.8
248  electric    4.4
249       spo    1.4
250  electric    4.9
251      trap    1.8
252  electric    6.4
253  electric    2.0
254  electric    3.6
255  electric    2.1
256  electric    5.6
257  electric    4.6
259  electric    2.2
260  electric    4.5
262  electric    1.0
263  electric    4.0
264  electric    5.5
265  electric    4.8
266  electric    1.0
267  electric    4.2
268  electric    3.4
269  electric    5.8
270  electric    4.2
271       net    2.5
272  electric    5.3
273  electric    4.1
275  electric    4.0
276  electric    4.5
277   mixture    1.6
278  electric    4.1
279  electric    3.4
280   mixture    1.0
281  electric    3.3
282  electric    3.3
283   mixture    1.0
286  electric    3.4
287  electric    5.2
289  electric    3.4
290  electric    4.8
291  electric    3.2
293  electric    4.5
294  electric    4.2
295       spo    5.1
296  electric    4.5
297  electric    4.3
298  electric    3.0
299       net    1.9
300  electric    1.4
302       net    2.5
303  electric    2.1
305  electric    3.9
306  electric    1.0
307       net    3.5
308  electric    3.1
309       spo    4.8
310       spo    4.6
312  electric    4.4
313  electric    4.8
314       net    2.6
315  electric    3.3
317  electric    4.2
320  electric    3.5
321  electric    4.8
323  electric    1.0
324  electric    1.2
325   mixture    1.0
326  electric    4.0
327  electric    4.0
329  electric    5.6
330  electric    3.7
333  electric    4.3
334  electric    4.7
335       spo    5.2
336  electric    3.7
337  electric    3.0
338  electric    3.4
339  electric    4.8
340  electric    2.2
341  electric    1.0
342  electric    2.2
343  electric    4.6
344       spo    5.3
345  electric    4.7
346  electric    3.8
347  electric    4.4
348   mixture    2.3
349  electric    4.3
351       net    4.5
353  electric    1.3
354  electric    3.3
355  electric    4.8
356  electric    3.0
358  electric    4.4
359  electric    3.4
360       spo    5.0
361  electric    2.5
362  electric    4.1
364  electric    1.0
365   mixture    4.0
366      trap    1.6
367  electric    3.5
369  electric    5.0
370  electric    3.7
371  electric    4.0
372  electric    4.8
373  electric    3.7
374  electric    3.4
375  electric    4.0
376  electric    3.8
377   mixture    2.2
378  electric    3.6
379  electric    5.0
380      trap    1.5
381  electric    4.7
382  electric    3.2
383  electric    5.2
384  electric    3.6
385  electric    5.0
386  electric    2.7
387  electric    3.9
388   mixture    1.7
389  electric    4.8
391      trap    4.0
392       net    2.2
393  electric    5.3
394      trap    4.4
395  electric    3.9
398  electric    5.3
399  electric    4.8
400  electric    4.3
401  electric    1.2
402      trap    1.0
403  electric    5.8
404  electric    4.8
405  electric    4.0
406  electric    5.0
407  electric    5.4
408  electric    3.6
409  electric    3.0
412  electric    4.5
413  electric    4.9
414  electric    1.7
415  electric    2.7
416      trap    1.2
417  electric    4.6
419       spo    2.6
420  electric    3.9
421  electric    4.1
423  electric    5.5
425  electric    3.1
426  electric    3.4
428  electric    4.5
430  electric    1.0
432  electric    4.9
433      trap    1.4
434  electric    3.5
435  electric    5.7
436   mixture    2.6
438  electric    5.3
439      trap    1.6
440  electric    4.5
441  electric    4.5
442  electric    3.8
443  electric    3.4
445  electric    1.0
447  electric    4.2
449  electric    4.2
450  electric    5.1
451  electric    2.1
453   mixture    4.4
454  electric    6.2
455  electric    4.2
456  electric    4.8
457  electric    1.8
458  electric    3.1
459       net    1.8
460  electric    4.3
461  electric    4.0
463  electric    2.6
465  electric    6.8
466  electric    5.6
468  electric    4.7
469       net    3.2
470  electric    5.1
471  electric    2.8
472  electric    2.0
473  electric    3.4
474  electric    2.6
475  electric    4.2
477  electric    4.7
479      trap    6.1
480  electric    3.0
481  electric    4.5
482  electric    3.7
485      trap    1.0
486  electric    4.8
487  electric    4.6
489  electric    3.5
490  electric    3.8
491  electric    1.8
492  electric    4.9
493      trap    2.4
495  electric    6.0
496  electric    4.3
497  electric    5.0
498  electric    5.0
499       spo    4.3
500  electric    4.8
501  electric    5.4
502  electric    3.8
503       net    1.5
504  electric    4.8
505  electric    3.8
506       spo    4.3
507  electric    5.0
508  electric    5.0
509  electric    3.5
510  electric    5.0
511  electric    4.7
513   mixture    1.0
514  electric    5.2
515  electric    4.1
517  electric    1.6
518  electric    4.8
519  electric    4.3
521  electric    3.6
522  electric    4.7
523       net    2.0
524  electric    1.4
526   mixture    2.0
527  electric    5.4
528  electric    5.4
529  electric    4.9
530   mixture    3.0
533  electric    3.3
534  electric    3.4
535  electric    4.1
536  electric    4.5
537  electric    4.8
538  electric    5.8
540  electric    1.3
541  electric    3.3
542  electric    5.2
543  electric    1.0
544   mixture    5.2
545  electric    5.6
547  electric    5.0
548  electric    1.5
549   mixture    4.1
550  electric    4.2
551  electric    3.0
552  electric    3.0
553  electric    3.6
554  electric    2.7
555  electric    1.6
556  electric    4.8
557      trap    1.2
558  electric    3.8
559  electric    3.1
560  electric    6.0
561  electric    4.0
563   mixture    1.0
566  electric    3.5
570  electric    2.2
571      trap    1.0
572  electric    3.6
574  electric    3.4
577       net    2.9
578  electric    4.3
579  electric    3.9
580  electric    3.1
581  electric    4.4
584   mixture    1.0
585       net    1.0
586  electric    1.0
588  electric    4.0
589  electric    3.5
590  electric    3.0
591  electric    5.8
592  electric    5.5
593  electric    4.2
594  electric    4.2
595  electric    5.8
596  electric    4.6
597  electric    2.1
598  electric    4.5
599  electric    3.6
600  electric    3.1
601  electric    5.0
602  electric    2.9
603  electric    5.1
604       net    5.0
605  electric    5.1
606  electric    4.2
607  electric    4.5
608       net    3.3
610  electric    5.3
611  electric    4.8
612  electric    4.2
613  electric    5.0
614  electric    3.2
615  electric    3.2
616  electric    3.6
618  electric    4.1
619  electric    3.2
620  electric    4.2
621  electric    2.5
624  electric    5.3
625  electric    6.4
626      trap    2.3
627  electric    4.3
631  electric    5.0
632  electric    5.3
634  electric    3.5
635  electric    4.3
636  electric    4.8
637  electric    5.5
638       spo    6.1
639  electric    3.2
640  electric    4.2
643   mixture    3.1
644  electric    2.8
645   mixture    2.9
646      trap    1.0
647  electric    2.6
648  electric    3.5
649  electric    4.5
650       spo    5.4
651   mixture    6.7
652  electric    3.2
653  electric    2.4
654  electric    5.8
655  electric    5.1
656  electric    4.7
657  electric    5.2
658  electric    4.9
659  electric    1.3
661  electric    7.0
662  electric    5.3
663  electric    4.0
664  electric    3.5
666  electric    1.6
667  electric    4.7
668  electric    4.8
670  electric    4.8
671  electric    4.3
672  electric    3.5
673  electric    4.0
674  electric    6.3
675  electric    2.4
676  electric    2.8
677  electric    4.9
678  electric    4.0
679  electric    1.5
680  electric    4.3
681  electric    4.9
683  electric    2.8
684  electric    4.8
685  electric    4.5
687  electric    5.2
689  electric    4.2
690  electric    5.2
691       net    2.6
692  electric    3.9
693   mixture    1.5
694  electric    1.2
696  electric    3.5
697  electric    3.8
699  electric    3.6
700       net    1.0
701  electric    4.8
702  electric    5.7
703  electric    2.2
704  electric    3.2
705       spo    5.2
706  electric    5.2
708  electric    2.2
709  electric    5.7
710  electric    1.8
711  electric    5.0
712  electric    4.4
713  electric    3.4
715  electric    4.5
716  electric    5.2
717  electric    3.6
718  electric    4.4
719  electric    4.0
720      trap    3.6
721  electric    6.5
722  electric    3.9
723  electric    3.1
724      trap    2.6
726  electric    5.2
727  electric    5.0
728  electric    4.2
729  electric    4.6
730  electric    4.6
731      trap    1.0
734  electric    5.4
735  electric    4.0
736  electric    2.6
737       net    4.2
738       net    3.8
739  electric    4.2
740  electric    4.5
741  electric    4.6
742   mixture    3.6
743  electric    3.8
745  electric    3.9
747   mixture    3.5
749       net    1.5
750       net    1.8
751  electric    3.4
752  electric    5.0
753  electric    4.2
754  electric    5.5
755  electric    4.7
756  electric    4.0
757  electric    4.2
758  electric    1.4
759  electric    4.3
760       spo    4.5
761       spo    3.6
762  electric    2.5
763  electric    3.4
764  electric    4.0
765      trap    2.4
766  electric    2.9
767  electric    1.2
768  electric    3.8
769  electric    3.2
771  electric    4.8
772  electric    3.8
773  electric    4.8
774  electric    4.9
775  electric    5.5
777  electric    4.2
779  electric    2.0
780   mixture    2.2
781  electric    4.7
782   mixture    6.8
783      trap    4.2
784  electric    4.0
785  electric    1.2
786  electric    4.4
788  electric    4.7
789       spo    4.2
790  electric    4.7
791  electric    4.8
792  electric    4.1
793       net    1.0
794  electric    5.3
795  electric    2.2
796  electric    3.9
797  electric    4.5
798  electric    2.9
799  electric    5.9
800  electric    3.3
801  electric    5.0
802  electric    4.5
804  electric    4.8
805       spo    4.2
806  electric    4.2
807  electric    5.5
808  electric    4.0
809  electric    3.9
810  electric    2.3
811      trap    1.4
812  electric    5.1
813       net    2.5
814       net    2.0
815  electric    3.6
816  electric    3.1
817  electric    4.5
818  electric    4.8
819  electric    4.7
820  electric    4.3
821  electric    3.5
822  electric    4.1
823  electric    3.4
824  electric    4.3
825  electric    4.5
826  electric    4.9
827      trap    1.0
828  electric    4.4
829  electric    4.7
830  electric    4.5
831  electric    3.5
833  electric    3.8
834  electric    5.1
836  electric    1.0
838  electric    4.4
839      trap    1.0
841  electric    3.8
842  electric    4.5
843       net    4.8
844  electric    5.2
845  electric    3.3
846  electric    4.0
847  electric    1.2
849  electric    3.5
850  electric    4.6
851   mixture    5.6
853  electric    5.5
854       spo    3.7
855      trap    3.8
857      trap    4.8
860  electric    5.4
862  electric    3.0
863  electric    1.5
864       spo    4.7
865  electric    6.9
866  electric    4.9
867  electric    3.6
868   mixture    1.0
869  electric    5.2
871  electric    4.2
872  electric    4.9
873  electric    3.5
875  electric    4.1
877       spo    3.5
878  electric    3.9
879  electric    5.0
880       spo    4.8
882  electric    1.4
883  electric    5.0
884       net    4.0
885  electric    4.6
886  electric    4.6
888  electric    3.5
890  electric    5.0
891  electric    1.0
892   mixture    1.0
893  electric    5.2
894  electric    4.3
896  electric    3.8
897  electric    4.5
898       spo    2.5
899  electric    5.0
901      trap    3.0
902  electric    4.7
903  electric    2.2
905  electric    3.4
906  electric    4.1
907  electric    3.6
908   mixture    1.0
909  electric    4.3
910  electric    3.6
911  electric    4.5
912  electric    5.8
913  electric    6.2
914  electric    3.8
916  electric    4.3
917  electric    5.5
918  electric    4.3
919  electric    4.3
920  electric    5.5
921      trap    3.3
923  electric    5.1
924       net    1.0
926  electric    6.8
927       net    1.9
928      trap    2.0
929  electric    4.3
930  electric    2.0
931  electric    4.6
932       net    2.8
933  electric    3.0
934  electric    4.7
935  electric    3.0
936  electric    3.4
937  electric    2.5
938  electric    5.5
939  electric    3.5
940  electric    3.5
941  electric    3.3
942       net    2.8
943   mixture    3.7
945  electric    4.8
946       spo    4.4
947  electric    4.1
948  electric    2.7
949       spo    4.7
950  electric    3.6
951   mixture    1.0
953  electric    5.2
954  electric    5.1
956  electric    4.0
958  electric    4.8
959  electric    5.4
960       spo    5.1
961  electric    4.8
962  electric    5.3
963  electric    4.5
966      trap    1.0
968  electric    4.0
969      trap    5.0
970  electric    5.4
971      trap    4.7
972  electric    4.3
973  electric    3.4
975  electric    4.4
976  electric    3.9
977  electric    3.2
978  electric    4.8
979       spo    5.1
980  electric    1.0
981  electric    5.6
983   mixture    7.0
984  electric    3.9
985  electric    4.2
986  electric    4.7
988  electric    5.5
989  electric    5.5
990  electric    2.6
991  electric    5.4
992       spo    1.8
993  electric    4.7
994  electric    4.2
995  electric    2.8
996  electric    5.5
997  electric    4.8
998       net    1.0
999       net    1.4
1000 electric    2.5

Test / train split

set.seed(20220908)
part = rsample::initial_split(anguilla, prop = 3/4)

anguilla_train = rsample::training(part)
anguilla_test  = rsample::testing(part)
dim(anguilla_train)
[1] 618  10
dim(anguilla_test)
[1] 206  10

EDA

EDA (part 1)

EDA (part 2)

EDA (part 3)

Basic Model

Model

g = glm(presence~SegSumT, family=binomial, data=anguilla_train)
summary(g)

Call:
glm(formula = presence ~ SegSumT, family = binomial, data = anguilla_train)

Coefficients:
             Estimate Std. Error z value Pr(>|z|)    
(Intercept) -15.02201    1.53770  -9.769   <2e-16 ***
SegSumT       0.80047    0.08726   9.173   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 627.81  on 617  degrees of freedom
Residual deviance: 501.93  on 616  degrees of freedom
AIC: 505.93

Number of Fisher Scoring iterations: 5

Fit

( g_pred = broom::augment(g, type.predict = "response") )
# A tibble: 618 × 8
   presence SegSumT .fitted .resid    .hat .sigma   .cooksd .std.resid
      <int>   <dbl>   <dbl>  <dbl>   <dbl>  <dbl>     <dbl>      <dbl>
 1        0    16.4  0.131  -0.529 0.00260  0.903 0.000197      -0.530
 2        1    17.1  0.209   1.77  0.00232  0.901 0.00443        1.77 
 3        0    14    0.0216 -0.209 0.00231  0.903 0.0000256     -0.209
 4        0    18.2  0.389  -0.992 0.00364  0.903 0.00117       -0.994
 5        0    15.6  0.0735 -0.391 0.00286  0.903 0.000114      -0.391
 6        0    18.3  0.408  -1.02  0.00395  0.902 0.00137       -1.03 
 7        0    18.5  0.447  -1.09  0.00466  0.902 0.00190       -1.09 
 8        0    16.2  0.114  -0.491 0.00270  0.903 0.000174      -0.492
 9        0    18    0.351  -0.930 0.00313  0.903 0.000853      -0.932
10        1    17.3  0.236   1.70  0.00233  0.901 0.00379        1.70 
# ℹ 608 more rows

Visually

Separation

ggplot(g_pred, aes(x=.fitted, y=presence, color=as.factor(presence))) +
  geom_jitter(height=0.1, alpha=0.5) +
  labs(color="presence")

Standard Residuals

g_std =  broom::augment(g, type.predict = "response") |>
  mutate(.resid = presence - .fitted)

Binned Residuals

bin_width = 0.05
g_std_bin = g_std |>
  mutate(bin = .fitted - (.fitted %% bin_width) + bin_width/2) |>
  group_by(bin) |>
  summarize(.resid_bin = mean(presence - .fitted))

Pearson Residuals

\[ r_i = \frac{Y_i - E(Y_i)}{\sqrt{Var(Y_i)}} = \frac{Y_i - \hat{p}_i}{\sqrt{\hat{p}_i(1-\hat{p}_i)}} \]

g_pearson = broom::augment(
  g, type.predict="response", 
  type.residuals="pearson"
)

Binned Pearson Residuals

g_pearson_bin = g_pearson |>
  mutate(bin = .fitted - (.fitted %% bin_width) + bin_width/2) |>
  group_by(bin) |>
  summarize(.resid_bin = mean(.resid))

Deviance Residuals

\[ \begin{aligned} d_i = &\text{sign}(Y_i-\hat{p_i}) \, \times \\ &\sqrt{ -2 \left(Y_i \log \hat{p}_i+(1-Y_i)\log (1 - \hat{p}_i) \right) } \end{aligned} \]

g_deviance = broom::augment(
  g, type.predict = "response", 
  type.residuals = "deviance"
)

Binned Deviance Residuals

g_deviance_bin = g_deviance |>
  mutate(bin = .fitted - (.fitted %% bin_width) + bin_width/2) |>
  group_by(bin) |>
  summarize(.resid_bin = mean(.resid))

Checking Deviance

g

Call:  glm(formula = presence ~ SegSumT, family = binomial, data = anguilla_train)

Coefficients:
(Intercept)      SegSumT  
   -15.0220       0.8005  

Degrees of Freedom: 617 Total (i.e. Null);  616 Residual
Null Deviance:      627.8 
Residual Deviance: 501.9    AIC: 505.9
summarize(g_deviance, sum(.resid^2))
# A tibble: 1 × 1
  `sum(.resid^2)`
            <dbl>
1            502.

Full Model

Model

f = glm(presence~., family=binomial, data=anguilla_train)
summary(f)

Call:
glm(formula = presence ~ ., family = binomial, data = anguilla_train)

Coefficients:
               Estimate Std. Error z value Pr(>|z|)    
(Intercept)   -9.352885   1.761202  -5.311 1.09e-07 ***
SegSumT        0.654186   0.096921   6.750 1.48e-11 ***
DSDist        -0.004837   0.002302  -2.102  0.03559 *  
DSMaxSlope    -0.030776   0.061995  -0.496  0.61959    
USRainDays    -0.710920   0.225814  -3.148  0.00164 ** 
USSlope       -0.069814   0.025443  -2.744  0.00607 ** 
USNative      -0.456598   0.455261  -1.003  0.31589    
DSDam         -1.095360   0.516960  -2.119  0.03410 *  
Methodmixture -0.430351   0.475411  -0.905  0.36535    
Methodnet     -0.066214   0.559162  -0.118  0.90574    
Methodspo     -1.583905   0.701902  -2.257  0.02403 *  
Methodtrap    -2.958398   0.688146  -4.299 1.72e-05 ***
LocSed        -0.140495   0.096849  -1.451  0.14688    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 627.81  on 617  degrees of freedom
Residual deviance: 426.96  on 605  degrees of freedom
AIC: 452.96

Number of Fisher Scoring iterations: 6

Separation

Residuals vs fitted

f_resid |>
  ggplot(aes(x=.fitted, y=.resid, color=type)) +
  geom_jitter(height=0.2, alpha=0.2) +
  facet_wrap(~type, ncol=3, scale="free_y") +
  geom_smooth(se = FALSE, color="black")

Residuals (binned) vs fitted

f_resid_bin |>
  mutate(type = as_factor(type)) |>
  ggplot(aes(x=bin, y=.resid_bin, color=type)) +
  geom_point() +
  facet_wrap(~type, ncol=3, scales = "free_y")